https://arxiv.org/abs/2601.15714

Skip to main content
Cornell University
Learn about arXiv becoming an independent nonprofit.
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2601.15714
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv logo
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Computer Science > Machine Learning

arXiv:2601.15714 (cs)
[Submitted on 22 Jan 2026]

Title:Even GPT-5.2 Can't Count to Five: The Case for Zero-Error
Horizons in Trustworthy LLMs

Authors:Ryoma Sato
View a PDF of the paper titled Even GPT-5.2 Can't Count to Five: The
Case for Zero-Error Horizons in Trustworthy LLMs, by Ryoma Sato
View PDF HTML (experimental)

    Abstract:We propose Zero-Error Horizon (ZEH) for trustworthy
    LLMs, which represents the maximum range that a model can solve
    without any errors. While ZEH itself is simple, we demonstrate
    that evaluating the ZEH of state-of-the-art LLMs yields abundant
    insights. For example, by evaluating the ZEH of GPT-5.2, we found
    that GPT-5.2 cannot even compute the parity of a short string
    like 11000, and GPT-5.2 cannot determine whether the parentheses
    in ((((()))))) are balanced. This is surprising given the
    excellent capabilities of GPT-5.2. The fact that LLMs make
    mistakes on such simple problems serves as an important lesson
    when applying LLMs to safety-critical domains. By applying ZEH to
    Qwen2.5 and conducting detailed analysis, we found that while ZEH
    correlates with accuracy, the detailed behaviors differ, and ZEH
    provides clues about the emergence of algorithmic capabilities.
    Finally, while computing ZEH incurs significant computational
    cost, we discuss how to mitigate this cost by achieving up to one
    order of magnitude speedup using tree structures and online
    softmax.

Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI);
          Computation and Language (cs.CL)
Cite as:  arXiv:2601.15714 [cs.LG]
          (or arXiv:2601.15714v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2601.15714
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Ryoma Sato [view email]
[v1] Thu, 22 Jan 2026 07:36:01 UTC (115 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Even GPT-5.2 Can't Count to Five:
    The Case for Zero-Error Horizons in Trustworthy LLMs, by Ryoma
    Sato
  * View PDF
  * HTML (experimental)
  * TeX Source

license icon view license
Current browse context:
cs.LG
< prev   |   next >
new | recent | 2026-01
Change to browse by:
cs
cs.AI
cs.CL

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

export BibTeX citation Loading...

BibTeX formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Reddit logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
[ ] scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
( ) Code, Data, Media

Code, Data and Media Associated with this Article

[ ] alphaXiv Toggle
alphaXiv (What is alphaXiv?)
[ ] Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
[ ] DagsHub Toggle
DagsHub (What is DagsHub?)
[ ] GotitPub Toggle
Gotit.pub (What is GotitPub?)
[ ] Huggingface Toggle
Hugging Face (What is Huggingface?)
[ ] Links to Code Toggle
Papers with Code (What is Papers with Code?)
[ ] ScienceCast Toggle
ScienceCast (What is ScienceCast?)
( ) Demos

Demos

[ ] Replicate Toggle
Replicate (What is Replicate?)
[ ] Spaces Toggle
Hugging Face Spaces (What is Spaces?)
[ ] Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
( ) Related Papers

Recommenders and Search Tools

[ ] Link to Influence Flower
Influence Flower (What are Influence Flowers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)
[ ] IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)

  * Author
  * Venue
  * Institution
  * Topic

( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status